If $A, B, C, D$ are the angles of a cyclic quadrilateral,then $\cos A + \cos B + \cos C + \cos D = $

The number of all possible values of $\theta$,where $0 < \theta < \pi$,for which the system of equations
$(y+z) \cos 3\theta = (xyz) \sin 3\theta$
$x \sin 3\theta = \frac{2 \cos 3\theta}{y} + \frac{2 \sin 3\theta}{z}$
$(xyz) \sin 3\theta = (y+2z) \cos 3\theta + y \sin 3\theta$
have a solution $(x_0, y_0, z_0)$ with $y_0 z_0 \neq 0$,is

If $\operatorname{Sinh}^{-1}(2)+\operatorname{Sinh}^{-1}(3)=\alpha$,then $\sinh \alpha=$

If $3 \cos \theta + 4 \sin \theta = 5$,then the value of $3 \sin \theta - 4 \cos \theta$ is:

If $\sin (\theta + \alpha ) = a$ and $\sin (\theta + \beta ) = b,$ then $\cos 2(\alpha - \beta ) - 4ab\cos (\alpha - \beta )$ is equal to

The equation $y = \sin \,x \sin \,(x + 2) - \sin^2 \,(x + 1)$ represents a straight line lying in